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Correlation and Related Dependency Concepts in Investment Management

Day One

Introduction to Correlation and Dependency Concepts

Stylized Facts about Correlations and Dependencies in Financial Market Data

  • Contagion effects in stock correlations
  • Globalization in global equity investing
  • Bonds as a safe haven asset
  • Is gold a safe haven?

Workshop: Calculating tail and downside correlations

Mathematical Properties of Correlation and the Correlation Matrix

  • Validity of a correlation matrix
  • Fixing a broken correlation matrix
  • Alternative correlation concepts
  • Spearman’s Rank Correlation
  • Kendall's T
  • Spectral decomposition of a correlation matrix: eigenvalues and eigenvectors
  • Singular value decomposition of correlations
  • Autocorrelation: dependency over time
  • Co-integration and its use in trading

Workshop: Examining the validity of a correlation matrix

Day Two

Correlation in Modern Portfolio Theory – Diversification

Scenario Analysis and Stress Testing

  • Tweaking individual entries in a correlation matrix
  • Changing blocks of correlation values
  • Extrapolating trends in correlations: "Risk On" and "Risk Off" scenarios
  • Randomizing a correlation matrix
  • Handling the additivity of conditional correlations

A General Theory of Dependency – Copulas

  • Introduction to Copula Theory
  • Applications of Copula Theory
    • Data analysis
    • Stress testing

Workshop: Identifying copulas in an international asset class universe

Simulating Correlated Data

  • Multivariant normal data
  • Solutions for non-normal data

Stochastic Process Models for the Correlation Coefficient

Forecasting Correlations

  • Historical estimators
  • Robust estimators
  • Bayesian shrinkage estimators: Jorion, Ledoit/Wolf
  • Implied correlations from derivatives instruments
  • Deriving asset correlations from factor correlations

Time Series Models for Correlations

  • Exponential smoothing
  • Multivariate GARCH
  • Dynamic Conditional Correlation (DCC)

Workshop: Analyzing the volatility risk of a multi-asset-class portfolio based on robust correlation scenarios  



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